Hughes 105 and Larkin 109 helped the Blues to 0-223 at stumps, trailing the Redbacks by 157 runs after bringing up their tons within an over of each other in the final half-hour of play.
The pair were operating on a pitch that offered little sign of life and took few chances after coming to the crease in the first session.
Coming into the day, the game was in the balance with the Redbacks at 5-315.
A damaging spell by Sean Abbott in the morning and the twin tons from the Blues' openers swung the game as the Redbacks were bowled out for 380.
Abbott (3-97) snared danger man Tom Cooper (89) and Nick Winter (0) in successive balls in the second over of the day.
Alex Carey made his second first-class century when he finished on 110 not out after wickets tumbled around him.
After Jake Lehmann and Jake Weatherald's first-day half-centuries, limited-overs Australian keeper Carey was the Redbacks' top-scorer.
Debutant Blues paceman Greg West finished with 3-88 after he helped Abbott to clean up the South Australian tail.
SA's bowlers toiled hard throughout the remainder of the day but were offered little assistance on a batter-friendly SCG pitch.